SOLUTION: Please help with the following problem where the directions read "Rationalize the following denominators - assume all variables to be positive" sq rt of 72 x^2 y^9 divided by aq

Question 78767: Please help with the following problem where the directions read "Rationalize the following denominators - assume all variables to be positive"
sq rt of 72 x^2 y^9 divided by aq rt of 49 x^7 y
Thanks so much!
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!

To rationalize the denominator, you need to multiply the denominator by itself. However, you cannot change the value of the entire fraction, so whatever you multiply the denominator by, you also need to multiply the numerator by the same thing:

Now you can rewrite this fraction with a rationalized denominator.

Now the fun part comes - simplifying this fraction. Let's tackle one square root at a time in the numerator...recognize that 72=2*2*2*3*3. That means you can pull out 2*3 or 6 from under the radical, and just leave the 2. Also, you can obviously pull out one x and y^4. Re-writing...

Now, looking at the second radical in the numerator, you know 49=7^2, so you can pull out a 7. Also, an x^3 can be pulled out as well. Rewriting...

the one simplification remaining is to cancel out one x from the numerator and denominator. I'll leave that part to you, I have typed enough already!
Good Luck,
tutor_paul@yahoo.com
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